Escape Probability for Stochastic Dynamical Systems with Jumps

Details Escape Probability for Stochastic Dynamical Systems with Jumps Escape Probability for Stochastic Dynamical Systems with Jumps

2011-11-28

arxiv.org/abs/1111.6419v1

Mathematics

Dynamical Systems

Scientific paper

The escape probability is a deterministic tool that quantifies some aspects of stochastic dynamics. This issue has been investigated extensively for dynamical systems driven by the Gaussian Brownian motion. The present work considers escape probabilities for dynamical systems driven by non-Gaussian L\'evy motions, especially symmetric $\alpha-$stable L\'evy motions. The escape probabilities are characterized as solutions of the Balayage-Dirichlet problems of certain differential-integral equations. Differences between escape probabilities for dynamical systems driven by Gaussian and non-Gaussian noises are highlighted. In certain special cases, analytic results for escape probabilities are given.

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